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pn is the ordinate of any point p on the parabola y^2=4x. if the normal at p to the parabola its axis at g then find ng.

pn is the ordinate of any point p on the parabola y^2=4x. if the normal at p to the parabola  its axis at g then find ng.
 

Grade:11

1 Answers

kkbisht
90 Points
3 years ago
Equation of normal at P (t2,2t) ( a parametric coordinate of a parabola y2=4x with vertex at origin) is given by  y +tx=2t+t3  Now this normal  meets the axis of parabola ( Y=0 ) at  0+tx=2t+t3 => x=2+t2 ( cancelling t)  .This is the point g i.e. og=2+t2 and the ordinate of the point P is 2t and the x-cordinte is t2 i.e on=t ( o is the origin as well as vertex of the parabola) therefore ng=og-on=2+t2-t2=2
therefore the length ng=2
 
kkbisht

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